1. Field of the Invention
This invention relates to analog circuits and, more particularly, to circuits for realizing preselected functions.
2. Description of the Prior Art
Quite often it is desirable to obtain a signal that relates to a driving signal in accordance with a particular function. Such a signal is generally obtained by applying the driving signal to a device or a network which is adapted to develop the desired signal in response to the driving signal. A device or a network capable of responding in such a manner realizes, it is commonly said, the particular function. An amplifier, for example, realizes the linear function because the input signal relates to the output signal in essentially a linear fashion. Many other functions are commonly realizable through a combination of various nonlinear devices, as taught, for example, in Wave Generation and Shaping by L. Strauss, McGraw-Hill, 1960.
Sometimes it is the inverse of a function which is desired. In situations where it is easier to obtain the function itself rather than its inverse, feedback is generally employed to derive the desired inverse function.
Redman, U.S. Pat. No. 3,987,366, issued Oct. 19, 1976, describes one such feedback circuit where the square root function is derived. In accordance with Redman, an input signal whose square root is desired is applied to the positive input terminal of a differential amplifier while the output signal of the amplifier is fed back to the negative input terminal of the differential amplifier through a squaring device. Since the negative input of the amplifier is forced to closely approximate the input signal, the output of the amplifier (which is connected to the squaring device) is forced to approximate the square root of the input signal.
The feedback technique described by Redman is quite robust but it has one drawback; the accuracy of the inverse function is dependent on the amplifier's gain. For stability and noise immunity reasons it might not be desirable to employ amplifiers with very large gains. In such situations, accuracy is sacrificed.